Also called map projection. Cartography. a systematic construction of lines drawn on a plane surface representative of and corresponding to the meridians and parallels of the curved surface of the earth or celestial sphere.

6.

Photography.

the act of reproducing on a surface, by optical means, a remote image on a film, slide, etc.

an image so reproduced.

7.

the act of visualizing and regarding an idea or the like as an objective reality.

late 15c., in alchemy, "transmutation by casting a powder on molten metal; 1550s in the cartographical sense "drawing of a map or chart according to scale," from Middle French projection, from Latin proiectionem (nominative proiectio), from past participle stem of proicere (see project (n.)). From 1590s as "action of projecting."

The image of a geometric figure reproduced on a line, plane, or surface.

A system of intersecting lines, such as the grid of a map, on which part or all of the globe or another spherical surface is represented as a plane surface. See more at azimuthal projection, conic projection, cylindrical projection.

theory In domain theory, a function, f, which is (a) idempotent, i.e. f(f(x))=f(x) and (b) whose result is no more defined than its argument. E.g. F(x)=bottom or F(x)=x. In reduction systems, a function which returns some component of its argument. E.g. head, tail, \ (x,y) . x. In a graph reduction system the function can just return a pointer to part of its argument and does not need to build any new graph. (1997-01-29)

in cartography, systematic representation on a flat surface of features of a curved surface, as that of the Earth. Such a representation presents an obvious problem but one that did not disturb ancient or medieval cartographers. Only when the voyages of exploration stimulated production of maps showing entire oceans, hemispheres, and the whole Earth did the question of projection come to the fore. Mercator produced the simplest and, for its purposes, the best solution by in effect converting the spherical Earth into a cylinder with the open ends at the poles; this cylinder was then opened to form a plane surface. East-west and north-south directions could be represented with fidelity, and the distortions in size became gross only near the polar regions (rendering Greenland, for example, disproportionately large). The Mercator projection is still widely used, especially when north-south dimensions are of chief importance. Many other projections are used, for example, the conic projection, drawn from a point directly above the North or South Pole. All projections involve some degree of distortion, and those showing the entire Earth involve a large degree